Using Value-at-Risk (VaR) to Measure Market Risk of the Equity Inventory of a Market Maker

We propose a simple approach to using value-at-risk (VaR) to measure market risk within the equity inventory of a market making entity, a task which presents several challenges specific to the market making function. Market makers constantly stand ready to buy and sell shares to market participants. In doing so, they inevitably maintain the inventory of shares, a portfolio of sorts, subject to market risk. VaR is a standard tool for measuring the market risk in investment portfolios, so a variety of calculation techniques have been developed over the years. However, the application of VaR to market making inventories requires a few adjustments, for unlike the typical investment portfolio these inventories change rapidly, as if they were rebalanced intra-day. Moreover, the number of unique tickers in the inventory for a given day may routinely list thousands of securities. As a result, at any moment in an inventory there could be hundreds of items with missing historical price data, which makes challenging the application of even the simplest VaR methods. The approach proposed in this paper deals with the rapidly rebalancing portfolio and missing data issues inherent in market making equity portfolios by rescaling portfolio weight to allow for the application of well-known VaR techniques to very large inventories.